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Full text of "Analytical Mechanics"

36                        ANALYTICAL MECHANICS
It is evident from Fig. 26 that a couple is capable of giving a rigid body a motion of rotation. But this is not enough to show that the effect produced by a couple is the same as that produced by a torque. Wo must show also that the couple is not capable of producing a motion of translation. Consider the rigid body A, FiR. 27, which is acted upon by a couple. Suppose the couple did tend to
FIG. 26.
FIG. 27.
produce a translation in a direction BBf. Then pass through the body a smooth bar of rectangular cross-section in the direction of the supposed motion, so that the body is free to move along the bar but not free to rotate. When this constraint is imposed upon the rigid body it behaves like a particle and therefore cannot be given a motion by two equal and opposite forces. But since any motion in the direction BB' is not affected by the presence of the bar, the assumption that the couple produces a motion of translation along BBr must be wrong. Hence we see that whoa the bar is taken out the motion due to the couple will be one of pure rotation.
43. Measure of Torque.  When a rigid body is in equilibrium under the action of two couples it is always found that the product of one of the forces of one couple by the distance apart of the forces of the same couple equals the